Integrated waveguide-coupled terahertz microcavity ... - Cornell ECE
APPLIED PHYSICS LETTERS 91, 191122 共2007兲
Integrated waveguide-coupled terahertz microcavity resonators Paul A. George,a兲 Christina Manolatou, and Farhan Rana School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA
Adam L. Bingham and Daniel R. Grischkowsky School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA
共Received 30 August 2007; accepted 22 October 2007; published online 9 November 2007兲 We demonstrate integrated square terahertz microcavity resonators side coupled to waveguides. We present the microcavity transmission spectra for different resonator sizes and coupling strengths. The measured quality factors due to external coupling and cavity loss are found to be between 40 and 90 and between 30 and 40, respectively, for cavity resonance frequencies between 1.077 and 1.331 THz. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2809608兴 Integrated terahertz photonic components are important for performing terahertz spectroscopy of vibrational modes in biological and chemical molecules,1 realizing lab-on-achip detection platforms with high sensitivity,2–4 and developing compact sources of coherent terahertz radiation.5,6 Although several types of passive terahertz waveguides and resonators have been experimentally demonstrated,7–9 they have typically been fabricated using bulk micromachining techniques and are not suitable for on-chip integration. In this letter, we experimentally demonstrate for the first time integrated terahertz air-core metallic square microcavity resonators side coupled to metal waveguides. At near-IR wavelengths, evanescent-field coupling is commonly used to excite dielectric microcavities via waveguides.10 Here, we demonstrate aperture coupling of air-core resonators to waveguides at terahertz frequencies. Strong field enhancement in air-core microcavity resonators can be used for narrowband sensing and the study of terahertz nonlinearities. We present measurements of the cavity quality factors resulting from external coupling and intrinsic cavity loss for different resonator sizes and find good agreement with calculations. Figure 1 shows a schematic of a square terahertz microcavity resonator, with side d, coupled to a waveguide via an aperture with width w and thickness t. The yˆ -polarized electric field propagates in the TE10 waveguide mode and excites the fundamental TE101 mode of the microcavity. Because the spatial profiles of the TE10 and TE101 modes are constant in the yˆ direction, the electromagnetic fields in these modes can be simulated using a two-dimensional finite-difference timedomain 共2D-FDTD兲 method. The simulated resonant terahertz electric field in the structure is shown in Fig. 1. The terahertz resonators and waveguides under test were fabricated from highly doped 3 in. Si wafers 共NA = 1020 cm−3兲 to avoid measuring terahertz radiation coupled to the substrate. First, one wafer was patterned and etched 150 m in an inductively coupled plasma deep-Si etcher. The 150 m etch depth established the waveguide, resonator, and aperture height 共dimension in the yˆ direction兲. A scanning electron microscopy 共SEM兲 image of a typical etched structure is shown in Fig. 2共a兲. As can be seen, the coupling aperture was etched anisotropically and was undera兲
Electronic mail: [email protected]
cut by 20 m. Next, both the etched and blank Si wafers were oxidized with 750 nm of thermal oxide. After oxidation, 50 nm of Ti and 400 nm of Au were uniformly deposited on the wafers using an e-beam evaporator with planetary rotation. The thickness of the Au layer was chosen to be greater than five electromagnetic skin depths 共⬃80 nm兲 at terahertz frequencies.11 Following evaporation, both wafers were pressed together to form a temporary bond. The wafer stack was then permanently bonded under vacuum on a wafer bonder at a temperature of 350 ° C and a pressure of 1.5 MPa for 45 min.12 Finally, the completed devices were diced to 7 mm long and the facets were polished until optically smooth at terahertz frequencies. Figure 2共b兲 displays one facet of an air-core rectangular metal waveguide. Terahertz measurements of the waveguides were conducted using a purged terahertz TD spectrometer 共TDS兲 with a semi-insulating–GaAs photoconductive transmitter and a silicon on sapphire photoconductive receiver.9 The spectrometer was pumped by an ultrafast Ti:sapphire laser and the power incident upon both the transmitter and receiver was 10 mW. With a lock-in amplifier time constant of 100 ms, the power spectral dynamic range of the experiments was 106. Terahertz radiation from the terahertz TDS was coupled into the devices using Si hyperhemispherical lenses butt coupled to each waveguide facet. Multiple scans of each device were performed to ensure the repeatability of spectral features resulting from the excitation of a microcavity.
FIG. 1. 共Color online兲 Schematic of a terahertz microcavity resonator side coupled to a metal waveguide overlayed with the simulated terahertz electric field from 2D-FDTD. The square resonator has side d and the coupling aperture has width w and thickness t. The terahertz electric field is polarized in yˆ direction and the waveguide is 200 m wide.
0003-6951/2007/91共19兲/191122/3/$23.00 91, 191122-1 © 2007 American Institute of Physics Downloaded 19 Feb 2008 to 128.84.87.77. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
191122-2
Appl. Phys. Lett. 91, 191122 共2007兲
George et al.
FIG. 2. 共Color online兲 共a兲 SEM of a fabricated terahertz resonator under test. 共b兲 Photograph of a polished waveguide facet which shows an air-core metal waveguide and Au–Au bond.
Three square resonators with sides d = 175, 150, and 125 m coupled to 200 m wide waveguides via apertures of average widths w = 110 and 100 m and thickness t = 10 m were measured using the terahertz TDS. As an example, the time-domain terahertz electric field after propagation through a waveguide coupled to a resonator 共d = 125 m and w = 100 m兲 is shown in Fig. 3. Ringing in the waveform due to waveguide dispersion as well as the frequency-dependent transmission of the resonator extend past 60 ps. Figure 3 also displays the measured power transmitted through the device. The transmission spectrum exhibits a narrow feature at 1.331 THz that corresponds to excitation of the resonant cavity. The strong oscillations in the spectrum that begin at 2.15 THz are characteristic of significant excitation of higher order waveguide modes.7 Near the resonant frequency, the evolution of the electric field b inside of a resonator coupled to a single-mode waveguide can be described by coupled mode theory,13
冉
冊 冑
1 1 db = j− − 0b + dt 2QL 2QE
0 ai . 2QE
共1兲
In Eq. 共1兲, 0 is the resonance frequency, QE and QL are the cavity quality factors related to external coupling and intrinsic cavity loss, respectively, and ai is the incident waveguide field 共Fig. 1兲 normalized such that its squared magnitude equals the incident power. The transmitted field is at, where at = ai − b冑0 / 2QE.13 After combining this equation with the time-harmonic solution to Eq. 共1兲, the expression obtained
FIG. 4. 共Color online兲 Microcavity transmission spectra for resonators with d = 175, 150, and 125 m and average w = 110 and 100 m. Measured values QE are between 40 and 90 and a data extraction error of less than 10% is expected.
for the frequency-dependent power transmission of the coupled waveguide-resonator system T共兲 is T共兲 =
冏冏 冏 at ai
2
= 1−
1/QE 1/QE + 1/QL − 2j共1 − /0兲
冏
2
. 共2兲
This expression has a Lorentzian shape and is applicable for frequencies close to 0. From Eq. 共2兲, it can be seen that the power transmission at resonance is reduced from unity and is exactly zero for lossless cavities 共QL = ⬁兲. This occurs because the electromagnetic radiation coupled from a lossless resonator back into the waveguide in the forward direction interferes completely destructively with the incident radiation ai. As shown in Fig. 4, the microcavities affect the measured terahertz TDS spectra only in a narrow frequency range near resonance. To extract the microcavity transmission spectra, the measured terahertz TDS spectra with resonances removed were fitted with fifth-order polynomials near
FIG. 3. Measured terahertz time-domain electric field waveform and accompanying power spectrum after propagation through a resonator structure 共d = 125 m and w = 100 m兲. The resonance dip at 1.331 THz is evidence of excitation of the resonator mode. Downloaded 19 Feb 2008 to 128.84.87.77. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
191122-3
Appl. Phys. Lett. 91, 191122 共2007兲
George et al.
TABLE I. Measured and simulated values of 0, QE, and QL for d = 175 m. Good agreement exists between the experimental and 2DFDTD results for 0 and QE. Large discrepancy in QL may be due to imperfect metallization and defects in the Au–Au bond. d 共m兲
w 共m兲
175 175
110 100
175 175
110 100
0 共THz兲
QE
QL
Measured 1.077 1.091
40 65
30 35
2D-FDTD 1.117 1.132
55 80
370 354
the resonance frequencies and the total terahertz TDS spectra were then normalized with these polynomials. Figure 4 shows the transmission spectra of different cavities obtained in this way. The Lorentzian expression in Eq. 共2兲 was fitted to the measured microcavity transmission spectra to obtain the values of 0, QE, and QL, which are also shown in Fig. 4. It can be seen that the measured transmission spectra are well described by a Lorentzian near the resonance frequency. The values of QE and QL changed by less than 10% when a third-order polynomial was used to extract the transmission spectra. The increase of 0 and QE with decrease in w matches closely the trends predicted by 2D-FDTD simulations. Table I shows the measured data and simulated results obtained from 2D-FDTD for d = 175 m and w averaged to account for the 20 m etch undercut mentioned previously. The small discrepancies between these measured and FDTD values can be attributed to nonidealities in the structure dimensions and sidewall verticality that cannot be modeled by twodimensional simulations. Similar agreement exists between FDTD results and experimental data for the other resonators shown in Fig. 4 共d = 150 and 125 m兲. As can be seen in Table I, the measured and simulated values of QL differ significantly. Using a conductivity of 38⫻ 106 S / m for Au at 1 THz,11,14 the calculated values of QL are between 291 and 370 for all the cavity geometries studied in this work. These values are significantly larger than the measured values of 30–40 presented in Fig. 4. This disagreement may partially be due to the reduced conductivity of evaporated Au at terahertz frequencies15 but is more likely attributable to defects in the Au–Au bond. Imperfections in the bond could lead to a contact resistance of several
ohms that would add in series with the resistance due to Ohmic losses in the cavity sidewalls 共⬃0.4 ⍀兲. The calculated values of QL agree well with the measured values if a bond resistance of ⬃3 ⍀ is assumed. In conclusion, we have demonstrated integrated terahertz microcavity resonators side coupled to metal waveguides. The extracted values of QE for these devices are between 40 and 90 and agree well with results from 2D-FDTD. However, the measured values of QL are much smaller than those predicted by simulations. From Eq. 共1兲, the estimated enhancement of the square magnitude of the peak terahertz electric field in the microcavity resonator to that in the waveguide is between 8 and 18 for all of the structures in this work. Achieving strong field enhancement in integrated structures would, therefore, require terahertz microcavities with small intrinsic cavity losses. Such structures would be well suited for narrowband sensing applications, developing integrated sources of terahertz radiation, and studying THz nonlinearities. This work was supported by the National Science Foundation. 1
D. L. Woolard, W. R. Loerep, and M. S. Shur, Terahertz Sensing Technology 共World Scientific, New Jersey, 2003兲, Vols. 1 and 2, p. 1. 2 J. S. Melinger, N. Laman, and S. S. Harsha, and D. Grischkowsky, Appl. Phys. Lett. 89, 251110 共2006兲. 3 M. Nagel, P. H. Bolívar, M. Bruscherseifer, H. Kurz, A. Bosserhoff, and R. Büttner, Appl. Opt. 41, 2074 共2002兲. 4 H. Kurt and D. S. Citrin, Appl. Phys. Lett. 87, 041108 共2005兲. 5 G. Fasching, A. Benz, K. Unterrainer, R. Zobl, A. M. Andrews, T. Roch, W. Schrenk, and G. Strasser, Appl. Phys. Lett. 87, 211112 共2005兲. 6 P. A. George, C. Manolatou, F. Rana, and A. I. Akinwande, Proceedings of the 2005 Conference on Lasers and Electro-Optics, 2005 共unpublished兲. Paper no. CThX5. 7 G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, J. Opt. Soc. Am. B 17, 851 共2000兲. 8 K. Wang and D. M. Mittleman, Nature 共London兲 432, 376 共2004兲. 9 A. L. Bingham and D. Grischkowsky, Appl. Phys. Lett. 90, 091105 共2007兲. 10 K. Vahala, Optical Microcavities 共World Scientific, New Jersey, 2004兲, Vol. 5, p. 9. 11 D. M. Pozar, Microwave Engineering, 3rd ed. 共Wiley, New Jersey, 2005兲, p. 687. 12 C. H. Tsau, S. M. Spearing, and M. A. Schmidt, J. Microelectromech. Syst. 11, 641 共2002兲. 13 C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 共1999兲. 14 B. Williams, H. Callebaut, S. Kumar, and Q. Hu, Appl. Phys. Lett. 82, 1015 共2003兲. 15 N. Laman and D. Grischkowsky, Appl. Phys. Lett. 90, 122115 共2007兲.
Downloaded 19 Feb 2008 to 128.84.87.77. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
Integrated waveguide-coupled terahertz microcavity resonators Paul A. George,a兲 Christina Manolatou, and Farhan Rana School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA
Adam L. Bingham and Daniel R. Grischkowsky School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA
共Received 30 August 2007; accepted 22 October 2007; published online 9 November 2007兲 We demonstrate integrated square terahertz microcavity resonators side coupled to waveguides. We present the microcavity transmission spectra for different resonator sizes and coupling strengths. The measured quality factors due to external coupling and cavity loss are found to be between 40 and 90 and between 30 and 40, respectively, for cavity resonance frequencies between 1.077 and 1.331 THz. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2809608兴 Integrated terahertz photonic components are important for performing terahertz spectroscopy of vibrational modes in biological and chemical molecules,1 realizing lab-on-achip detection platforms with high sensitivity,2–4 and developing compact sources of coherent terahertz radiation.5,6 Although several types of passive terahertz waveguides and resonators have been experimentally demonstrated,7–9 they have typically been fabricated using bulk micromachining techniques and are not suitable for on-chip integration. In this letter, we experimentally demonstrate for the first time integrated terahertz air-core metallic square microcavity resonators side coupled to metal waveguides. At near-IR wavelengths, evanescent-field coupling is commonly used to excite dielectric microcavities via waveguides.10 Here, we demonstrate aperture coupling of air-core resonators to waveguides at terahertz frequencies. Strong field enhancement in air-core microcavity resonators can be used for narrowband sensing and the study of terahertz nonlinearities. We present measurements of the cavity quality factors resulting from external coupling and intrinsic cavity loss for different resonator sizes and find good agreement with calculations. Figure 1 shows a schematic of a square terahertz microcavity resonator, with side d, coupled to a waveguide via an aperture with width w and thickness t. The yˆ -polarized electric field propagates in the TE10 waveguide mode and excites the fundamental TE101 mode of the microcavity. Because the spatial profiles of the TE10 and TE101 modes are constant in the yˆ direction, the electromagnetic fields in these modes can be simulated using a two-dimensional finite-difference timedomain 共2D-FDTD兲 method. The simulated resonant terahertz electric field in the structure is shown in Fig. 1. The terahertz resonators and waveguides under test were fabricated from highly doped 3 in. Si wafers 共NA = 1020 cm−3兲 to avoid measuring terahertz radiation coupled to the substrate. First, one wafer was patterned and etched 150 m in an inductively coupled plasma deep-Si etcher. The 150 m etch depth established the waveguide, resonator, and aperture height 共dimension in the yˆ direction兲. A scanning electron microscopy 共SEM兲 image of a typical etched structure is shown in Fig. 2共a兲. As can be seen, the coupling aperture was etched anisotropically and was undera兲
Electronic mail: [email protected]
cut by 20 m. Next, both the etched and blank Si wafers were oxidized with 750 nm of thermal oxide. After oxidation, 50 nm of Ti and 400 nm of Au were uniformly deposited on the wafers using an e-beam evaporator with planetary rotation. The thickness of the Au layer was chosen to be greater than five electromagnetic skin depths 共⬃80 nm兲 at terahertz frequencies.11 Following evaporation, both wafers were pressed together to form a temporary bond. The wafer stack was then permanently bonded under vacuum on a wafer bonder at a temperature of 350 ° C and a pressure of 1.5 MPa for 45 min.12 Finally, the completed devices were diced to 7 mm long and the facets were polished until optically smooth at terahertz frequencies. Figure 2共b兲 displays one facet of an air-core rectangular metal waveguide. Terahertz measurements of the waveguides were conducted using a purged terahertz TD spectrometer 共TDS兲 with a semi-insulating–GaAs photoconductive transmitter and a silicon on sapphire photoconductive receiver.9 The spectrometer was pumped by an ultrafast Ti:sapphire laser and the power incident upon both the transmitter and receiver was 10 mW. With a lock-in amplifier time constant of 100 ms, the power spectral dynamic range of the experiments was 106. Terahertz radiation from the terahertz TDS was coupled into the devices using Si hyperhemispherical lenses butt coupled to each waveguide facet. Multiple scans of each device were performed to ensure the repeatability of spectral features resulting from the excitation of a microcavity.
FIG. 1. 共Color online兲 Schematic of a terahertz microcavity resonator side coupled to a metal waveguide overlayed with the simulated terahertz electric field from 2D-FDTD. The square resonator has side d and the coupling aperture has width w and thickness t. The terahertz electric field is polarized in yˆ direction and the waveguide is 200 m wide.
0003-6951/2007/91共19兲/191122/3/$23.00 91, 191122-1 © 2007 American Institute of Physics Downloaded 19 Feb 2008 to 128.84.87.77. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
191122-2
Appl. Phys. Lett. 91, 191122 共2007兲
George et al.
FIG. 2. 共Color online兲 共a兲 SEM of a fabricated terahertz resonator under test. 共b兲 Photograph of a polished waveguide facet which shows an air-core metal waveguide and Au–Au bond.
Three square resonators with sides d = 175, 150, and 125 m coupled to 200 m wide waveguides via apertures of average widths w = 110 and 100 m and thickness t = 10 m were measured using the terahertz TDS. As an example, the time-domain terahertz electric field after propagation through a waveguide coupled to a resonator 共d = 125 m and w = 100 m兲 is shown in Fig. 3. Ringing in the waveform due to waveguide dispersion as well as the frequency-dependent transmission of the resonator extend past 60 ps. Figure 3 also displays the measured power transmitted through the device. The transmission spectrum exhibits a narrow feature at 1.331 THz that corresponds to excitation of the resonant cavity. The strong oscillations in the spectrum that begin at 2.15 THz are characteristic of significant excitation of higher order waveguide modes.7 Near the resonant frequency, the evolution of the electric field b inside of a resonator coupled to a single-mode waveguide can be described by coupled mode theory,13
冉
冊 冑
1 1 db = j− − 0b + dt 2QL 2QE
0 ai . 2QE
共1兲
In Eq. 共1兲, 0 is the resonance frequency, QE and QL are the cavity quality factors related to external coupling and intrinsic cavity loss, respectively, and ai is the incident waveguide field 共Fig. 1兲 normalized such that its squared magnitude equals the incident power. The transmitted field is at, where at = ai − b冑0 / 2QE.13 After combining this equation with the time-harmonic solution to Eq. 共1兲, the expression obtained
FIG. 4. 共Color online兲 Microcavity transmission spectra for resonators with d = 175, 150, and 125 m and average w = 110 and 100 m. Measured values QE are between 40 and 90 and a data extraction error of less than 10% is expected.
for the frequency-dependent power transmission of the coupled waveguide-resonator system T共兲 is T共兲 =
冏冏 冏 at ai
2
= 1−
1/QE 1/QE + 1/QL − 2j共1 − /0兲
冏
2
. 共2兲
This expression has a Lorentzian shape and is applicable for frequencies close to 0. From Eq. 共2兲, it can be seen that the power transmission at resonance is reduced from unity and is exactly zero for lossless cavities 共QL = ⬁兲. This occurs because the electromagnetic radiation coupled from a lossless resonator back into the waveguide in the forward direction interferes completely destructively with the incident radiation ai. As shown in Fig. 4, the microcavities affect the measured terahertz TDS spectra only in a narrow frequency range near resonance. To extract the microcavity transmission spectra, the measured terahertz TDS spectra with resonances removed were fitted with fifth-order polynomials near
FIG. 3. Measured terahertz time-domain electric field waveform and accompanying power spectrum after propagation through a resonator structure 共d = 125 m and w = 100 m兲. The resonance dip at 1.331 THz is evidence of excitation of the resonator mode. Downloaded 19 Feb 2008 to 128.84.87.77. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
191122-3
Appl. Phys. Lett. 91, 191122 共2007兲
George et al.
TABLE I. Measured and simulated values of 0, QE, and QL for d = 175 m. Good agreement exists between the experimental and 2DFDTD results for 0 and QE. Large discrepancy in QL may be due to imperfect metallization and defects in the Au–Au bond. d 共m兲
w 共m兲
175 175
110 100
175 175
110 100
0 共THz兲
QE
QL
Measured 1.077 1.091
40 65
30 35
2D-FDTD 1.117 1.132
55 80
370 354
the resonance frequencies and the total terahertz TDS spectra were then normalized with these polynomials. Figure 4 shows the transmission spectra of different cavities obtained in this way. The Lorentzian expression in Eq. 共2兲 was fitted to the measured microcavity transmission spectra to obtain the values of 0, QE, and QL, which are also shown in Fig. 4. It can be seen that the measured transmission spectra are well described by a Lorentzian near the resonance frequency. The values of QE and QL changed by less than 10% when a third-order polynomial was used to extract the transmission spectra. The increase of 0 and QE with decrease in w matches closely the trends predicted by 2D-FDTD simulations. Table I shows the measured data and simulated results obtained from 2D-FDTD for d = 175 m and w averaged to account for the 20 m etch undercut mentioned previously. The small discrepancies between these measured and FDTD values can be attributed to nonidealities in the structure dimensions and sidewall verticality that cannot be modeled by twodimensional simulations. Similar agreement exists between FDTD results and experimental data for the other resonators shown in Fig. 4 共d = 150 and 125 m兲. As can be seen in Table I, the measured and simulated values of QL differ significantly. Using a conductivity of 38⫻ 106 S / m for Au at 1 THz,11,14 the calculated values of QL are between 291 and 370 for all the cavity geometries studied in this work. These values are significantly larger than the measured values of 30–40 presented in Fig. 4. This disagreement may partially be due to the reduced conductivity of evaporated Au at terahertz frequencies15 but is more likely attributable to defects in the Au–Au bond. Imperfections in the bond could lead to a contact resistance of several
ohms that would add in series with the resistance due to Ohmic losses in the cavity sidewalls 共⬃0.4 ⍀兲. The calculated values of QL agree well with the measured values if a bond resistance of ⬃3 ⍀ is assumed. In conclusion, we have demonstrated integrated terahertz microcavity resonators side coupled to metal waveguides. The extracted values of QE for these devices are between 40 and 90 and agree well with results from 2D-FDTD. However, the measured values of QL are much smaller than those predicted by simulations. From Eq. 共1兲, the estimated enhancement of the square magnitude of the peak terahertz electric field in the microcavity resonator to that in the waveguide is between 8 and 18 for all of the structures in this work. Achieving strong field enhancement in integrated structures would, therefore, require terahertz microcavities with small intrinsic cavity losses. Such structures would be well suited for narrowband sensing applications, developing integrated sources of terahertz radiation, and studying THz nonlinearities. This work was supported by the National Science Foundation. 1
D. L. Woolard, W. R. Loerep, and M. S. Shur, Terahertz Sensing Technology 共World Scientific, New Jersey, 2003兲, Vols. 1 and 2, p. 1. 2 J. S. Melinger, N. Laman, and S. S. Harsha, and D. Grischkowsky, Appl. Phys. Lett. 89, 251110 共2006兲. 3 M. Nagel, P. H. Bolívar, M. Bruscherseifer, H. Kurz, A. Bosserhoff, and R. Büttner, Appl. Opt. 41, 2074 共2002兲. 4 H. Kurt and D. S. Citrin, Appl. Phys. Lett. 87, 041108 共2005兲. 5 G. Fasching, A. Benz, K. Unterrainer, R. Zobl, A. M. Andrews, T. Roch, W. Schrenk, and G. Strasser, Appl. Phys. Lett. 87, 211112 共2005兲. 6 P. A. George, C. Manolatou, F. Rana, and A. I. Akinwande, Proceedings of the 2005 Conference on Lasers and Electro-Optics, 2005 共unpublished兲. Paper no. CThX5. 7 G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, J. Opt. Soc. Am. B 17, 851 共2000兲. 8 K. Wang and D. M. Mittleman, Nature 共London兲 432, 376 共2004兲. 9 A. L. Bingham and D. Grischkowsky, Appl. Phys. Lett. 90, 091105 共2007兲. 10 K. Vahala, Optical Microcavities 共World Scientific, New Jersey, 2004兲, Vol. 5, p. 9. 11 D. M. Pozar, Microwave Engineering, 3rd ed. 共Wiley, New Jersey, 2005兲, p. 687. 12 C. H. Tsau, S. M. Spearing, and M. A. Schmidt, J. Microelectromech. Syst. 11, 641 共2002兲. 13 C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 共1999兲. 14 B. Williams, H. Callebaut, S. Kumar, and Q. Hu, Appl. Phys. Lett. 82, 1015 共2003兲. 15 N. Laman and D. Grischkowsky, Appl. Phys. Lett. 90, 122115 共2007兲.
Downloaded 19 Feb 2008 to 128.84.87.77. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
